mailitics

Tag: convergence

  • Efficient Uncoupled Learning Dynamics with $tilde{O}!left(T^{-1/4}right)$ Last-Iterate Convergence in Bilinear Saddle-Point Problems over Convex Sets under Bandit Feedback

    Efficient Uncoupled Learning Dynamics with $tilde{O}!left(T^{-1/4}right)$ Last-Iterate Convergence in Bilinear Saddle-Point Problems over Convex Sets under Bandit Feedback arXiv:2602.21436v1 Announce Type: new Abstract: In this paper, we study last-iterate convergence of learning algorithms in bilinear saddle-point problems, a preferable notion of convergence that captures the day-to-day behavior of learning dynamics. We focus on the challenging…

  • Stationary Reweighting Yields Local Convergence of Soft Fitted Q-Iteration

    Stationary Reweighting Yields Local Convergence of Soft Fitted Q-Iteration arXiv:2512.23927v1 Announce Type: new Abstract: Fitted Q-iteration (FQI) and its entropy-regularized variant, soft FQI, are central tools for value-based model-free offline reinforcement learning, but can behave poorly under function approximation and distribution shift. In the entropy-regularized setting, we show that the soft Bellman operator is locally…

  • Convergence of off-policy TD(0) with linear function approximation for reversible Markov chains

    Convergence of off-policy TD(0) with linear function approximation for reversible Markov chains arXiv:2510.25514v1 Announce Type: new Abstract: We study the convergence of off-policy TD(0) with linear function approximation when used to approximate the expected discounted reward in a Markov chain. It is well known that the combination of off-policy learning and function approximation can lead…

  • Exponential Convergence Guarantees for Iterative Markovian Fitting

    Exponential Convergence Guarantees for Iterative Markovian Fitting arXiv:2510.20871v1 Announce Type: new Abstract: The Schr”odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting (IMF) have been proposed-alongside practical approximations like Diffusion Schr”odinger Bridge and…

  • A Short Note on Upper Bounds for Graph Neural Operator Convergence Rate

    A Short Note on Upper Bounds for Graph Neural Operator Convergence Rate arXiv:2510.20954v1 Announce Type: new Abstract: Graphons, as limits of graph sequences, provide a framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons yields operator-level convergence rates, enabling transferability analyses of GNNs. This note summarizes known…

  • Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift

    Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift arXiv:2509.05106v1 Announce Type: new Abstract: This paper investigates the convergence properties of spectral algorithms — a class of regularization methods originating from inverse problems — under covariate shift. In this setting, the marginal distributions of inputs differ between source and target domains, while the conditional distribution…

  • Uniform convergence for Gaussian kernel ridge regression

    Uniform convergence for Gaussian kernel ridge regression arXiv:2508.11274v1 Announce Type: new Abstract: This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where…

  • From Sublinear to Linear: Fast Convergence in Deep Networks via Locally Polyak-Lojasiewicz Regions

    From Sublinear to Linear: Fast Convergence in Deep Networks via Locally Polyak-Lojasiewicz Regions arXiv:2507.21429v1 Announce Type: new Abstract: The convergence of gradient descent (GD) on the non-convex loss landscapes of deep neural networks (DNNs) presents a fundamental theoretical challenge. While recent work has established that GD converges to a stationary point at a sublinear rate…

  • Optimal Convergence Rates of Deep Neural Network Classifiers

    Optimal Convergence Rates of Deep Neural Network Classifiers arXiv:2506.14899v1 Announce Type: new Abstract: In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s in [0,infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of…

  • Exponential Convergence of CAVI for Bayesian PCA

    Exponential Convergence of CAVI for Bayesian PCA arXiv:2505.16145v1 Announce Type: new Abstract: Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is allowing uncertainty quantification. The parameters of BPCA are typically learned using…

  • On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces

    On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces arXiv:2504.13623v1 Announce Type: new Abstract: We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove…

  • On the Convergence and Stability of Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers

    On the Convergence and Stability of Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers arXiv:2502.05672v1 Announce Type: new Abstract: This article provides a rigorous analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning and Online Decision Transformers. These algorithms performed competitively across various benchmarks, from games to robotic tasks,…

  • Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models

    Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models arXiv:2501.18863v1 Announce Type: new Abstract: Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based…

  • On the convergence of noisy Bayesian Optimization with Expected Improvement

    On the convergence of noisy Bayesian Optimization with Expected Improvement arXiv:2501.09262v1 Announce Type: new Abstract: Expected improvement (EI) is one of the most widely-used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors and rates for EI. In this paper, we…

  • Random Sparse Lifts: Construction, Analysis and Convergence of finite sparse networks

    Random Sparse Lifts: Construction, Analysis and Convergence of finite sparse networks arXiv:2501.05930v1 Announce Type: cross Abstract: We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global optimality of non-convex…